How to generate a set of random points within a given (x,y) coordinates in an x-y plane?

This might give you some ideas:

from random import random
import math
def rand_cluster(n,c,r):
    """returns n random points in disk of radius r centered at c"""
    x,y = c
    points = []
    for i in range(n):
        theta = 2*math.pi*random()
        s = r*random()
        points.append((x+s*math.cos(theta), y+s*math.sin(theta)))
    return points

This function can be used in various ways, for example:

def rand_clusters(k,n,r, a,b,c,d):
    """return k clusters of n points each in random disks of radius r
where the centers of the disk are chosen randomly in [a,b]x[c,d]"""
    clusters = []
    for _ in range(k):
        x = a + (b-a)*random()
        y = c + (d-c)*random()
        clusters.extend(rand_cluster(n,(x,y),r))
    return clusters

A typical all would look like

clusters = rand_clusters(4,50,0.3,0,1,0,1)

This generates 4 clusters of size 50 of radius 0.3 with centers chosen at random in the unit square. Points from a typical run:

If you generate data using

min + (max - min) * random()

Then they will be between min and max.

Do this for x and y, and for every cluster.